Thank you all for the answers:
I wondered how could it be, that I overlooked this simple solution:
Export[..., Background -> None],
when I realized, I didn't. Actually, when saving any graphics object
with this method indeed produces
transparent background, *however* importing the result into Corel
Photopaint X3 the figure does show up with
a solid black background. That was the cause that made me write the
post. It was pure chance that once I opened Photopaint X4 instead of
X3 by mistake, I discovered that the background is indeed transparent.
So it seems
that it is a Corel X3 issue: it does not support alpha channels for
PNG files.
Istv=E1n